# For Teachers: Grading Tests for Formative Assessment

So this is my first blog post targeted towards other teachers of mathematics.  The other dozens and dozens of posts are targeted towards my students and our Badging system.  But I’m going to start writing a few more posts to help other math teachers see some of the effective things I’m doing in my classroom and see if they want to consider maybe adopting them in their own practices.  I’m inspired by a lot of the great things I’ve found in the Math Twitter Blogosphere #MTBoS and a lot of the great folks I’ve met as part of that community.

So today, I’m going to talk about how I grade my tests.  I *so badly* want my tests to be more than just a number that describes my students’ level of understanding.  I truly believe that tests can be another tool of formative assessment, just like informal check-ins.  After all, if we truly believe that math is cumulative in nature, can’t test and exam results also be used to help student understanding as we move forward?

I’ve adopted a pretty simple technique that allows students to see the types of mistakes they’re making quickly and identify areas for improvement.  I color-code their errors.

Here’s what you’ll need:  http://www.officedepot.com/a/products/508624/Office-Depot-Brand-Liquid-Ink-Highlighters/  :

These Foray brand highlighters are great for writing and also serve well for highlighting errors.  There are a dozen in a box, so you can get through 4 tests/exams per box of highlighters.

Choose three highlighters per test, and assign them as “Careless”, “Arithmetic”, or “Understanding”.

Depending on the type of mistake you see the students making, highlight/mark the mistake in the color you’ve designated for that type of mistake.  For example, here is a student who made two mistakes on a single question, but I can designate which type of mistake she made:

Neither are critical errors — a dropped negative sign moving from one step to the next, and an error in integer arithmetic.

More significantly, students can see when they seem to have a lack of understanding in an area:

This student broke Order of Operations by trying to deal with a subtraction sign incorrectly.  That’s a significant error in understanding of exponents, subtraction, grouping symbols, etc.  They should spend some time addressing that mistake.

Here’s the key, though — when tests are returned, there should be time set aside in class for analysis of errors.  Students may not agree with my color choice for a particular mistake, and they should be given a chance to reflect on the different types of mistakes and determine whether or not they agree with my analysis.  I’ve had students tell me “I really did understand this, but I was careless with my negative sign” or something similar.  The point is not whether or not I was “right” in analyzing their error, the point is that the student is spending time thinking about what type of mistake they made on the test.

I also require students to formulate a plan for any errors in understanding.  So in the examples above, I would say “If you see any Green highlighter on the test, and you agree with my analysis that it was an error in understanding — what are you going to do about it?  What’s your plan to address that moving forward?”

I love that this grading system emphasizes to the students that tests are not a stopping point.  They’re not a period at the end of their learning, they’re more of a semi-colon.  There’s still work to be done *after* the assessment, and the assessment itself provides feedback on how to continue to grow and improve.

Teachers — if you like this idea, please consider sharing it with your colleagues, and please consider posting a comment below if you adopted this strategy and let us all know how it went.

Look for more blog posts like this using the Category links below (#MTBoS, For Teachers)

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